%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : ALG039+1 : TPTP v8.1.2. Released v2.7.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Aug 30 16:35:48 EDT 2023 % Result : Theorem 8.06s 1.91s % Output : Proof 12.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG039+1 : TPTP v8.1.2. Released v2.7.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n026.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Mon Aug 28 05:18:34 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.85/1.30 Prover 1: Preprocessing ... % 4.06/1.33 Prover 4: Preprocessing ... % 4.22/1.37 Prover 3: Preprocessing ... % 4.22/1.37 Prover 5: Preprocessing ... % 4.22/1.37 Prover 6: Preprocessing ... % 4.22/1.37 Prover 2: Preprocessing ... % 4.22/1.37 Prover 0: Preprocessing ... % 6.87/1.74 Prover 3: Constructing countermodel ... % 6.87/1.74 Prover 6: Constructing countermodel ... % 6.87/1.75 Prover 4: Constructing countermodel ... % 6.87/1.75 Prover 1: Constructing countermodel ... % 7.24/1.77 Prover 0: Constructing countermodel ... % 7.24/1.78 Prover 2: Constructing countermodel ... % 8.06/1.91 Prover 3: proved (1294ms) % 8.06/1.91 % 8.06/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.06/1.91 % 8.06/1.91 Prover 2: stopped % 8.06/1.92 Prover 6: proved (1291ms) % 8.06/1.92 % 8.06/1.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.06/1.92 % 8.06/1.93 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.06/1.93 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.06/1.93 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.06/1.93 Prover 0: stopped % 8.46/1.94 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.05/2.02 Prover 8: Preprocessing ... % 9.05/2.03 Prover 10: Preprocessing ... % 9.05/2.05 Prover 7: Preprocessing ... % 9.44/2.09 Prover 11: Preprocessing ... % 9.44/2.10 Prover 8: Constructing countermodel ... % 9.44/2.12 Prover 5: Constructing countermodel ... % 9.44/2.12 Prover 5: stopped % 10.11/2.15 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.11/2.22 Prover 13: Preprocessing ... % 10.47/2.36 Prover 10: Constructing countermodel ... % 10.47/2.37 Prover 11: Constructing countermodel ... % 11.71/2.38 Prover 7: Constructing countermodel ... % 11.71/2.38 Prover 4: Found proof (size 92) % 11.71/2.38 Prover 4: proved (1764ms) % 11.71/2.38 Prover 8: stopped % 11.71/2.38 Prover 13: Constructing countermodel ... % 11.71/2.38 Prover 11: stopped % 11.71/2.38 Prover 7: stopped % 11.71/2.39 Prover 10: stopped % 11.83/2.39 Prover 1: Found proof (size 92) % 11.83/2.39 Prover 1: proved (1775ms) % 11.83/2.39 Prover 13: stopped % 11.83/2.39 % 11.83/2.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.83/2.39 % 11.83/2.41 % SZS output start Proof for theBenchmark % 11.83/2.41 Assumptions after simplification: % 11.83/2.41 --------------------------------- % 11.83/2.41 % 11.83/2.41 (ax1) % 12.00/2.45 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.00/2.45 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 12.00/2.45 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 12.00/2.45 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & % 12.00/2.45 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & % 12.00/2.45 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & % 12.00/2.45 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 12.00/2.45 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 12.00/2.45 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 12.00/2.45 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 = % 12.00/2.45 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 | % 12.00/2.45 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 % 12.00/2.45 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | % 12.00/2.45 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | % 12.00/2.45 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | % 12.00/2.45 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 12.00/2.45 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3 % 12.00/2.45 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1 % 12.00/2.45 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0)) % 12.00/2.45 % 12.00/2.45 (ax3) % 12.00/2.46 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.00/2.46 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 12.00/2.46 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 12.00/2.46 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & % 12.00/2.46 op(e3, e1) = v11 & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & % 12.00/2.46 op(e2, e1) = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & % 12.00/2.46 op(e1, e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 12.00/2.46 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 12.00/2.46 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 12.00/2.46 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 = e3 | v11 = e3 | v6 = % 12.00/2.46 e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = e3) & (v15 = e2 | v14 = e2 | % 12.00/2.46 v11 = e2 | v6 = e2) & (v15 = e2 | v13 = e2 | v9 = e2 | v3 = e2) & (v15 = % 12.00/2.46 e1 | v14 = e1 | v11 = e1 | v6 = e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 % 12.00/2.46 = e1) & (v15 = e0 | v14 = e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 % 12.00/2.46 | v9 = e0 | v3 = e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = % 12.00/2.46 e2 | v12 = e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = % 12.00/2.46 e1) & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 | % 12.00/2.46 v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & (v13 = % 12.00/2.46 e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | v10 = e0 | v5 % 12.00/2.46 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & (v11 = e2 | v10 = e2 | % 12.00/2.46 v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 = e1 | v1 = e1) & (v11 = e0 % 12.00/2.46 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = e3 | v8 = e3 | v7 = e3 | v4 = e3) % 12.00/2.46 & (v9 = e2 | v8 = e2 | v7 = e2 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | % 12.00/2.46 v4 = e1) & (v9 = e0 | v8 = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | % 12.00/2.46 v4 = e3 | v0 = e3) & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | % 12.00/2.46 v5 = e1 | v4 = e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & % 12.00/2.46 (v3 = e2 | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 % 12.00/2.46 = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = e0 | % 12.00/2.46 v1 = e0)))) % 12.00/2.46 % 12.00/2.46 (ax4) % 12.00/2.47 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.00/2.47 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 12.00/2.47 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: % 12.00/2.47 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ % 12.00/2.47 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = % 12.00/2.47 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & % 12.00/2.47 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 = % 12.00/2.47 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~ % 12.00/2.47 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) & % 12.00/2.47 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) & % 12.00/2.47 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) & % 12.00/2.47 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ % 12.00/2.47 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ % 12.00/2.47 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = % 12.00/2.47 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = % 12.00/2.47 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9 % 12.00/2.47 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 & % 12.00/2.47 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) & % 12.00/2.47 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 12.00/2.47 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.00/2.47 % 12.00/2.47 (ax6) % 12.00/2.47 op(e3, e1) = e2 & op(e1, e1) = e0 & $i(e3) & $i(e2) & $i(e1) & $i(e0) % 12.00/2.47 % 12.00/2.47 (co1) % 12.00/2.47 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : % 12.00/2.47 ? [v3: $i] : (op(e3, e3) = v3 & op(e2, e2) = v2 & op(e1, e1) = v1 & op(e0, e0) % 12.00/2.47 = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = e3) | ~ (v2 = e3) | ~ % 12.00/2.47 (v1 = e3) | ~ (v0 = e3)) & ( ~ (v3 = e2) | ~ (v2 = e2) | ~ (v1 = e2) | % 12.00/2.47 ~ (v0 = e2)) & ( ~ (v3 = e1) | ~ (v2 = e1) | ~ (v1 = e1) | ~ (v0 = e1)) % 12.00/2.47 & ( ~ (v3 = e0) | ~ (v2 = e0) | ~ (v1 = e0) | ~ (v0 = e0)) & ((v3 = e3 & % 12.00/2.47 v2 = e3 & v1 = e3 & v0 = e3) | (v3 = e2 & v2 = e2 & v1 = e2 & v0 = e2) | % 12.00/2.47 (v3 = e1 & v2 = e1 & v1 = e1 & v0 = e1) | (v3 = e0 & v2 = e0 & v1 = e0 & % 12.00/2.47 v0 = e0))) % 12.00/2.47 % 12.00/2.47 (function-axioms) % 12.00/2.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3, % 12.00/2.47 v2) = v1) | ~ (op(v3, v2) = v0)) % 12.00/2.47 % 12.00/2.47 Further assumptions not needed in the proof: % 12.00/2.47 -------------------------------------------- % 12.00/2.47 ax2, ax5 % 12.00/2.47 % 12.00/2.47 Those formulas are unsatisfiable: % 12.00/2.47 --------------------------------- % 12.00/2.47 % 12.00/2.47 Begin of proof % 12.00/2.47 | % 12.00/2.47 | ALPHA: (ax1) implies: % 12.00/2.48 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.00/2.48 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 12.00/2.48 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 12.00/2.48 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13 % 12.00/2.48 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1) % 12.00/2.48 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1, % 12.00/2.48 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 12.00/2.48 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & % 12.00/2.48 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 12.00/2.48 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 % 12.00/2.48 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 % 12.00/2.48 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 | % 12.00/2.48 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 | % 12.00/2.48 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3 % 12.00/2.48 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8 % 12.00/2.48 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 = % 12.00/2.48 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) & % 12.00/2.48 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = % 12.00/2.48 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 % 12.00/2.48 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 % 12.00/2.48 | = e0)) % 12.00/2.48 | % 12.00/2.48 | ALPHA: (ax3) implies: % 12.00/2.49 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.00/2.49 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 12.00/2.49 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 12.00/2.49 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v11 % 12.00/2.49 | & op(e3, e0) = v6 & op(e2, e3) = v13 & op(e2, e2) = v12 & op(e2, e1) % 12.00/2.49 | = v10 & op(e2, e0) = v5 & op(e1, e3) = v9 & op(e1, e2) = v8 & op(e1, % 12.00/2.49 | e1) = v7 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 & % 12.00/2.49 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & % 12.00/2.49 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & % 12.00/2.49 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v14 % 12.00/2.49 | = e3 | v11 = e3 | v6 = e3) & (v15 = e3 | v13 = e3 | v9 = e3 | v3 = % 12.00/2.49 | e3) & (v15 = e2 | v14 = e2 | v11 = e2 | v6 = e2) & (v15 = e2 | v13 % 12.00/2.49 | = e2 | v9 = e2 | v3 = e2) & (v15 = e1 | v14 = e1 | v11 = e1 | v6 = % 12.00/2.49 | e1) & (v15 = e1 | v13 = e1 | v9 = e1 | v3 = e1) & (v15 = e0 | v14 = % 12.00/2.49 | e0 | v11 = e0 | v6 = e0) & (v15 = e0 | v13 = e0 | v9 = e0 | v3 = % 12.00/2.49 | e0) & (v14 = e3 | v12 = e3 | v8 = e3 | v2 = e3) & (v14 = e2 | v12 = % 12.00/2.49 | e2 | v8 = e2 | v2 = e2) & (v14 = e1 | v12 = e1 | v8 = e1 | v2 = e1) % 12.00/2.49 | & (v14 = e0 | v12 = e0 | v8 = e0 | v2 = e0) & (v13 = e3 | v12 = e3 | % 12.00/2.49 | v10 = e3 | v5 = e3) & (v13 = e2 | v12 = e2 | v10 = e2 | v5 = e2) & % 12.00/2.49 | (v13 = e1 | v12 = e1 | v10 = e1 | v5 = e1) & (v13 = e0 | v12 = e0 | % 12.00/2.49 | v10 = e0 | v5 = e0) & (v11 = e3 | v10 = e3 | v7 = e3 | v1 = e3) & % 12.00/2.49 | (v11 = e2 | v10 = e2 | v7 = e2 | v1 = e2) & (v11 = e1 | v10 = e1 | v7 % 12.00/2.49 | = e1 | v1 = e1) & (v11 = e0 | v10 = e0 | v7 = e0 | v1 = e0) & (v9 = % 12.00/2.49 | e3 | v8 = e3 | v7 = e3 | v4 = e3) & (v9 = e2 | v8 = e2 | v7 = e2 | % 12.00/2.49 | v4 = e2) & (v9 = e1 | v8 = e1 | v7 = e1 | v4 = e1) & (v9 = e0 | v8 % 12.00/2.49 | = e0 | v7 = e0 | v4 = e0) & (v6 = e3 | v5 = e3 | v4 = e3 | v0 = e3) % 12.00/2.49 | & (v6 = e2 | v5 = e2 | v4 = e2 | v0 = e2) & (v6 = e1 | v5 = e1 | v4 = % 12.00/2.49 | e1 | v0 = e1) & (v3 = e3 | v2 = e3 | v1 = e3 | v0 = e3) & (v3 = e2 % 12.00/2.49 | | v2 = e2 | v1 = e2 | v0 = e2) & (v3 = e1 | v2 = e1 | v1 = e1 | v0 % 12.00/2.49 | = e1) & (v0 = e0 | ((v6 = e0 | v5 = e0 | v4 = e0) & (v3 = e0 | v2 = % 12.00/2.49 | e0 | v1 = e0)))) % 12.00/2.49 | % 12.00/2.49 | ALPHA: (ax4) implies: % 12.00/2.49 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : % 12.00/2.49 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ? % 12.00/2.49 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] : % 12.00/2.49 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~ % 12.00/2.49 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~ % 12.00/2.49 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~ % 12.00/2.49 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 % 12.00/2.49 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = % 12.00/2.49 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) % 12.00/2.49 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ % 12.00/2.49 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) % 12.00/2.49 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 % 12.00/2.49 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) & % 12.00/2.49 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 = % 12.00/2.49 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3, % 12.00/2.49 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 & % 12.00/2.49 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = % 12.00/2.49 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, % 12.00/2.49 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & % 12.00/2.49 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & % 12.00/2.49 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 12.00/2.49 | % 12.00/2.49 | ALPHA: (ax6) implies: % 12.00/2.50 | (4) op(e1, e1) = e0 % 12.00/2.50 | % 12.00/2.50 | ALPHA: (co1) implies: % 12.00/2.50 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (op(e3, e3) = % 12.00/2.50 | v3 & op(e2, e2) = v2 & op(e1, e1) = v1 & op(e0, e0) = v0 & $i(v3) & % 12.00/2.50 | $i(v2) & $i(v1) & $i(v0) & ( ~ (v3 = e3) | ~ (v2 = e3) | ~ (v1 = % 12.00/2.50 | e3) | ~ (v0 = e3)) & ( ~ (v3 = e2) | ~ (v2 = e2) | ~ (v1 = e2) % 12.00/2.50 | | ~ (v0 = e2)) & ( ~ (v3 = e1) | ~ (v2 = e1) | ~ (v1 = e1) | ~ % 12.00/2.50 | (v0 = e1)) & ( ~ (v3 = e0) | ~ (v2 = e0) | ~ (v1 = e0) | ~ (v0 = % 12.00/2.50 | e0)) & ((v3 = e3 & v2 = e3 & v1 = e3 & v0 = e3) | (v3 = e2 & v2 = % 12.00/2.50 | e2 & v1 = e2 & v0 = e2) | (v3 = e1 & v2 = e1 & v1 = e1 & v0 = e1) % 12.00/2.50 | | (v3 = e0 & v2 = e0 & v1 = e0 & v0 = e0))) % 12.00/2.50 | % 12.00/2.50 | DELTA: instantiating (5) with fresh symbols all_4_0, all_4_1, all_4_2, all_4_3 % 12.00/2.50 | gives: % 12.00/2.50 | (6) op(e3, e3) = all_4_0 & op(e2, e2) = all_4_1 & op(e1, e1) = all_4_2 & % 12.00/2.50 | op(e0, e0) = all_4_3 & $i(all_4_0) & $i(all_4_1) & $i(all_4_2) & % 12.00/2.50 | $i(all_4_3) & ( ~ (all_4_0 = e3) | ~ (all_4_1 = e3) | ~ (all_4_2 = % 12.00/2.50 | e3) | ~ (all_4_3 = e3)) & ( ~ (all_4_0 = e2) | ~ (all_4_1 = e2) | % 12.00/2.50 | ~ (all_4_2 = e2) | ~ (all_4_3 = e2)) & ( ~ (all_4_0 = e1) | ~ % 12.00/2.50 | (all_4_1 = e1) | ~ (all_4_2 = e1) | ~ (all_4_3 = e1)) & ( ~ % 12.00/2.50 | (all_4_0 = e0) | ~ (all_4_1 = e0) | ~ (all_4_2 = e0) | ~ (all_4_3 % 12.00/2.50 | = e0)) & ((all_4_0 = e3 & all_4_1 = e3 & all_4_2 = e3 & all_4_3 = % 12.00/2.50 | e3) | (all_4_0 = e2 & all_4_1 = e2 & all_4_2 = e2 & all_4_3 = e2) | % 12.00/2.50 | (all_4_0 = e1 & all_4_1 = e1 & all_4_2 = e1 & all_4_3 = e1) | % 12.00/2.50 | (all_4_0 = e0 & all_4_1 = e0 & all_4_2 = e0 & all_4_3 = e0)) % 12.00/2.50 | % 12.00/2.50 | ALPHA: (6) implies: % 12.00/2.50 | (7) op(e1, e1) = all_4_2 % 12.00/2.50 | (8) (all_4_0 = e3 & all_4_1 = e3 & all_4_2 = e3 & all_4_3 = e3) | (all_4_0 % 12.00/2.50 | = e2 & all_4_1 = e2 & all_4_2 = e2 & all_4_3 = e2) | (all_4_0 = e1 & % 12.00/2.50 | all_4_1 = e1 & all_4_2 = e1 & all_4_3 = e1) | (all_4_0 = e0 & all_4_1 % 12.00/2.50 | = e0 & all_4_2 = e0 & all_4_3 = e0) % 12.00/2.50 | (9) ~ (all_4_0 = e0) | ~ (all_4_1 = e0) | ~ (all_4_2 = e0) | ~ (all_4_3 % 12.00/2.50 | = e0) % 12.00/2.50 | % 12.00/2.50 | DELTA: instantiating (3) with fresh symbols all_6_0, all_6_1, all_6_2, % 12.00/2.50 | all_6_3, all_6_4, all_6_5, all_6_6, all_6_7, all_6_8, all_6_9, % 12.00/2.50 | all_6_10, all_6_11, all_6_12, all_6_13, all_6_14, all_6_15 gives: % 12.00/2.50 | (10) ~ (all_6_0 = all_6_1) & ~ (all_6_0 = all_6_2) & ~ (all_6_0 = % 12.00/2.51 | all_6_3) & ~ (all_6_0 = all_6_4) & ~ (all_6_0 = all_6_8) & ~ % 12.00/2.51 | (all_6_0 = all_6_12) & ~ (all_6_1 = all_6_2) & ~ (all_6_1 = all_6_3) % 12.00/2.51 | & ~ (all_6_1 = all_6_5) & ~ (all_6_1 = all_6_9) & ~ (all_6_1 = % 12.00/2.51 | all_6_13) & ~ (all_6_2 = all_6_3) & ~ (all_6_2 = all_6_6) & ~ % 12.00/2.51 | (all_6_2 = all_6_10) & ~ (all_6_2 = all_6_14) & ~ (all_6_3 = % 12.00/2.51 | all_6_7) & ~ (all_6_3 = all_6_11) & ~ (all_6_3 = all_6_15) & ~ % 12.00/2.51 | (all_6_4 = all_6_5) & ~ (all_6_4 = all_6_6) & ~ (all_6_4 = all_6_7) % 12.00/2.51 | & ~ (all_6_4 = all_6_8) & ~ (all_6_4 = all_6_12) & ~ (all_6_5 = % 12.00/2.51 | all_6_6) & ~ (all_6_5 = all_6_7) & ~ (all_6_5 = all_6_9) & ~ % 12.00/2.51 | (all_6_5 = all_6_13) & ~ (all_6_6 = all_6_7) & ~ (all_6_6 = % 12.00/2.51 | all_6_10) & ~ (all_6_6 = all_6_14) & ~ (all_6_7 = all_6_11) & ~ % 12.00/2.51 | (all_6_7 = all_6_15) & ~ (all_6_8 = all_6_9) & ~ (all_6_8 = % 12.00/2.51 | all_6_10) & ~ (all_6_8 = all_6_11) & ~ (all_6_8 = all_6_12) & ~ % 12.00/2.51 | (all_6_9 = all_6_10) & ~ (all_6_9 = all_6_11) & ~ (all_6_9 = % 12.00/2.51 | all_6_13) & ~ (all_6_10 = all_6_11) & ~ (all_6_10 = all_6_14) & ~ % 12.00/2.51 | (all_6_11 = all_6_15) & ~ (all_6_12 = all_6_13) & ~ (all_6_12 = % 12.00/2.51 | all_6_14) & ~ (all_6_12 = all_6_15) & ~ (all_6_13 = all_6_14) & ~ % 12.00/2.51 | (all_6_13 = all_6_15) & ~ (all_6_14 = all_6_15) & op(e3, e3) = % 12.00/2.51 | all_6_0 & op(e3, e2) = all_6_4 & op(e3, e1) = all_6_8 & op(e3, e0) = % 12.00/2.51 | all_6_12 & op(e2, e3) = all_6_1 & op(e2, e2) = all_6_5 & op(e2, e1) = % 12.00/2.51 | all_6_9 & op(e2, e0) = all_6_13 & op(e1, e3) = all_6_2 & op(e1, e2) = % 12.00/2.51 | all_6_6 & op(e1, e1) = all_6_10 & op(e1, e0) = all_6_14 & op(e0, e3) = % 12.00/2.51 | all_6_3 & op(e0, e2) = all_6_7 & op(e0, e1) = all_6_11 & op(e0, e0) = % 12.00/2.51 | all_6_15 & $i(all_6_0) & $i(all_6_1) & $i(all_6_2) & $i(all_6_3) & % 12.00/2.51 | $i(all_6_4) & $i(all_6_5) & $i(all_6_6) & $i(all_6_7) & $i(all_6_8) & % 12.00/2.51 | $i(all_6_9) & $i(all_6_10) & $i(all_6_11) & $i(all_6_12) & % 12.00/2.51 | $i(all_6_13) & $i(all_6_14) & $i(all_6_15) % 12.00/2.51 | % 12.00/2.51 | ALPHA: (10) implies: % 12.41/2.51 | (11) op(e1, e1) = all_6_10 % 12.41/2.51 | % 12.41/2.51 | DELTA: instantiating (1) with fresh symbols all_8_0, all_8_1, all_8_2, % 12.41/2.51 | all_8_3, all_8_4, all_8_5, all_8_6, all_8_7, all_8_8, all_8_9, % 12.41/2.51 | all_8_10, all_8_11, all_8_12, all_8_13, all_8_14, all_8_15 gives: % 12.41/2.51 | (12) op(e3, e3) = all_8_0 & op(e3, e2) = all_8_1 & op(e3, e1) = all_8_2 & % 12.41/2.51 | op(e3, e0) = all_8_3 & op(e2, e3) = all_8_4 & op(e2, e2) = all_8_5 & % 12.41/2.51 | op(e2, e1) = all_8_6 & op(e2, e0) = all_8_7 & op(e1, e3) = all_8_8 & % 12.41/2.51 | op(e1, e2) = all_8_9 & op(e1, e1) = all_8_10 & op(e1, e0) = all_8_11 & % 12.41/2.51 | op(e0, e3) = all_8_12 & op(e0, e2) = all_8_13 & op(e0, e1) = all_8_14 % 12.41/2.51 | & op(e0, e0) = all_8_15 & $i(all_8_0) & $i(all_8_1) & $i(all_8_2) & % 12.41/2.51 | $i(all_8_3) & $i(all_8_4) & $i(all_8_5) & $i(all_8_6) & $i(all_8_7) & % 12.41/2.51 | $i(all_8_8) & $i(all_8_9) & $i(all_8_10) & $i(all_8_11) & $i(all_8_12) % 12.41/2.51 | & $i(all_8_13) & $i(all_8_14) & $i(all_8_15) & (all_8_0 = e3 | all_8_0 % 12.41/2.51 | = e2 | all_8_0 = e1 | all_8_0 = e0) & (all_8_1 = e3 | all_8_1 = e2 | % 12.41/2.51 | all_8_1 = e1 | all_8_1 = e0) & (all_8_2 = e3 | all_8_2 = e2 | % 12.41/2.51 | all_8_2 = e1 | all_8_2 = e0) & (all_8_3 = e3 | all_8_3 = e2 | % 12.41/2.51 | all_8_3 = e1 | all_8_3 = e0) & (all_8_4 = e3 | all_8_4 = e2 | % 12.41/2.51 | all_8_4 = e1 | all_8_4 = e0) & (all_8_5 = e3 | all_8_5 = e2 | % 12.41/2.51 | all_8_5 = e1 | all_8_5 = e0) & (all_8_6 = e3 | all_8_6 = e2 | % 12.41/2.51 | all_8_6 = e1 | all_8_6 = e0) & (all_8_7 = e3 | all_8_7 = e2 | % 12.41/2.51 | all_8_7 = e1 | all_8_7 = e0) & (all_8_8 = e3 | all_8_8 = e2 | % 12.41/2.51 | all_8_8 = e1 | all_8_8 = e0) & (all_8_9 = e3 | all_8_9 = e2 | % 12.41/2.51 | all_8_9 = e1 | all_8_9 = e0) & (all_8_10 = e3 | all_8_10 = e2 | % 12.41/2.51 | all_8_10 = e1 | all_8_10 = e0) & (all_8_11 = e3 | all_8_11 = e2 | % 12.41/2.51 | all_8_11 = e1 | all_8_11 = e0) & (all_8_12 = e3 | all_8_12 = e2 | % 12.41/2.51 | all_8_12 = e1 | all_8_12 = e0) & (all_8_13 = e3 | all_8_13 = e2 | % 12.41/2.51 | all_8_13 = e1 | all_8_13 = e0) & (all_8_14 = e3 | all_8_14 = e2 | % 12.41/2.51 | all_8_14 = e1 | all_8_14 = e0) & (all_8_15 = e3 | all_8_15 = e2 | % 12.41/2.51 | all_8_15 = e1 | all_8_15 = e0) % 12.41/2.51 | % 12.41/2.51 | ALPHA: (12) implies: % 12.41/2.51 | (13) op(e1, e1) = all_8_10 % 12.41/2.51 | % 12.41/2.51 | DELTA: instantiating (2) with fresh symbols all_10_0, all_10_1, all_10_2, % 12.41/2.51 | all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8, all_10_9, % 12.41/2.51 | all_10_10, all_10_11, all_10_12, all_10_13, all_10_14, all_10_15 gives: % 12.41/2.51 | (14) op(e3, e3) = all_10_0 & op(e3, e2) = all_10_1 & op(e3, e1) = all_10_4 % 12.41/2.51 | & op(e3, e0) = all_10_9 & op(e2, e3) = all_10_2 & op(e2, e2) = % 12.41/2.51 | all_10_3 & op(e2, e1) = all_10_5 & op(e2, e0) = all_10_10 & op(e1, e3) % 12.41/2.51 | = all_10_6 & op(e1, e2) = all_10_7 & op(e1, e1) = all_10_8 & op(e1, % 12.41/2.51 | e0) = all_10_11 & op(e0, e3) = all_10_12 & op(e0, e2) = all_10_13 & % 12.41/2.51 | op(e0, e1) = all_10_14 & op(e0, e0) = all_10_15 & $i(all_10_0) & % 12.41/2.51 | $i(all_10_1) & $i(all_10_2) & $i(all_10_3) & $i(all_10_4) & % 12.41/2.51 | $i(all_10_5) & $i(all_10_6) & $i(all_10_7) & $i(all_10_8) & % 12.41/2.51 | $i(all_10_9) & $i(all_10_10) & $i(all_10_11) & $i(all_10_12) & % 12.41/2.51 | $i(all_10_13) & $i(all_10_14) & $i(all_10_15) & (all_10_0 = e3 | % 12.41/2.51 | all_10_1 = e3 | all_10_4 = e3 | all_10_9 = e3) & (all_10_0 = e3 | % 12.41/2.51 | all_10_2 = e3 | all_10_6 = e3 | all_10_12 = e3) & (all_10_0 = e2 | % 12.41/2.51 | all_10_1 = e2 | all_10_4 = e2 | all_10_9 = e2) & (all_10_0 = e2 | % 12.41/2.51 | all_10_2 = e2 | all_10_6 = e2 | all_10_12 = e2) & (all_10_0 = e1 | % 12.41/2.51 | all_10_1 = e1 | all_10_4 = e1 | all_10_9 = e1) & (all_10_0 = e1 | % 12.41/2.51 | all_10_2 = e1 | all_10_6 = e1 | all_10_12 = e1) & (all_10_0 = e0 | % 12.41/2.51 | all_10_1 = e0 | all_10_4 = e0 | all_10_9 = e0) & (all_10_0 = e0 | % 12.41/2.51 | all_10_2 = e0 | all_10_6 = e0 | all_10_12 = e0) & (all_10_1 = e3 | % 12.41/2.51 | all_10_3 = e3 | all_10_7 = e3 | all_10_13 = e3) & (all_10_1 = e2 | % 12.41/2.51 | all_10_3 = e2 | all_10_7 = e2 | all_10_13 = e2) & (all_10_1 = e1 | % 12.41/2.51 | all_10_3 = e1 | all_10_7 = e1 | all_10_13 = e1) & (all_10_1 = e0 | % 12.41/2.51 | all_10_3 = e0 | all_10_7 = e0 | all_10_13 = e0) & (all_10_2 = e3 | % 12.41/2.51 | all_10_3 = e3 | all_10_5 = e3 | all_10_10 = e3) & (all_10_2 = e2 | % 12.41/2.51 | all_10_3 = e2 | all_10_5 = e2 | all_10_10 = e2) & (all_10_2 = e1 | % 12.41/2.51 | all_10_3 = e1 | all_10_5 = e1 | all_10_10 = e1) & (all_10_2 = e0 | % 12.41/2.52 | all_10_3 = e0 | all_10_5 = e0 | all_10_10 = e0) & (all_10_4 = e3 | % 12.41/2.52 | all_10_5 = e3 | all_10_8 = e3 | all_10_14 = e3) & (all_10_4 = e2 | % 12.41/2.52 | all_10_5 = e2 | all_10_8 = e2 | all_10_14 = e2) & (all_10_4 = e1 | % 12.41/2.52 | all_10_5 = e1 | all_10_8 = e1 | all_10_14 = e1) & (all_10_4 = e0 | % 12.41/2.52 | all_10_5 = e0 | all_10_8 = e0 | all_10_14 = e0) & (all_10_6 = e3 | % 12.41/2.52 | all_10_7 = e3 | all_10_8 = e3 | all_10_11 = e3) & (all_10_6 = e2 | % 12.41/2.52 | all_10_7 = e2 | all_10_8 = e2 | all_10_11 = e2) & (all_10_6 = e1 | % 12.41/2.52 | all_10_7 = e1 | all_10_8 = e1 | all_10_11 = e1) & (all_10_6 = e0 | % 12.41/2.52 | all_10_7 = e0 | all_10_8 = e0 | all_10_11 = e0) & (all_10_9 = e3 | % 12.41/2.52 | all_10_10 = e3 | all_10_11 = e3 | all_10_15 = e3) & (all_10_9 = e2 | % 12.41/2.52 | all_10_10 = e2 | all_10_11 = e2 | all_10_15 = e2) & (all_10_9 = e1 | % 12.41/2.52 | all_10_10 = e1 | all_10_11 = e1 | all_10_15 = e1) & (all_10_12 = e3 % 12.41/2.52 | | all_10_13 = e3 | all_10_14 = e3 | all_10_15 = e3) & (all_10_12 = % 12.41/2.52 | e2 | all_10_13 = e2 | all_10_14 = e2 | all_10_15 = e2) & (all_10_12 % 12.41/2.52 | = e1 | all_10_13 = e1 | all_10_14 = e1 | all_10_15 = e1) & % 12.41/2.52 | (all_10_15 = e0 | ((all_10_9 = e0 | all_10_10 = e0 | all_10_11 = e0) & % 12.41/2.52 | (all_10_12 = e0 | all_10_13 = e0 | all_10_14 = e0))) % 12.41/2.52 | % 12.41/2.52 | ALPHA: (14) implies: % 12.41/2.52 | (15) op(e1, e1) = all_10_8 % 12.41/2.52 | % 12.41/2.52 | GROUND_INST: instantiating (function-axioms) with all_6_10, all_8_10, e1, e1, % 12.41/2.52 | simplifying with (11), (13) gives: % 12.41/2.52 | (16) all_8_10 = all_6_10 % 12.41/2.52 | % 12.41/2.52 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_8_10, e1, e1, % 12.41/2.52 | simplifying with (7), (13) gives: % 12.41/2.52 | (17) all_8_10 = all_4_2 % 12.41/2.52 | % 12.41/2.52 | GROUND_INST: instantiating (function-axioms) with all_8_10, all_10_8, e1, e1, % 12.41/2.52 | simplifying with (13), (15) gives: % 12.41/2.52 | (18) all_10_8 = all_8_10 % 12.41/2.52 | % 12.41/2.52 | GROUND_INST: instantiating (function-axioms) with e0, all_10_8, e1, e1, % 12.41/2.52 | simplifying with (4), (15) gives: % 12.41/2.52 | (19) all_10_8 = e0 % 12.41/2.52 | % 12.41/2.52 | COMBINE_EQS: (18), (19) imply: % 12.41/2.52 | (20) all_8_10 = e0 % 12.41/2.52 | % 12.41/2.52 | SIMP: (20) implies: % 12.41/2.52 | (21) all_8_10 = e0 % 12.41/2.52 | % 12.41/2.52 | COMBINE_EQS: (16), (21) imply: % 12.41/2.52 | (22) all_6_10 = e0 % 12.41/2.52 | % 12.41/2.52 | COMBINE_EQS: (16), (17) imply: % 12.41/2.52 | (23) all_6_10 = all_4_2 % 12.41/2.52 | % 12.41/2.52 | COMBINE_EQS: (22), (23) imply: % 12.41/2.52 | (24) all_4_2 = e0 % 12.41/2.52 | % 12.41/2.52 | SIMP: (24) implies: % 12.41/2.52 | (25) all_4_2 = e0 % 12.41/2.52 | % 12.41/2.52 | BETA: splitting (8) gives: % 12.41/2.52 | % 12.41/2.52 | Case 1: % 12.41/2.52 | | % 12.41/2.52 | | (26) (all_4_0 = e3 & all_4_1 = e3 & all_4_2 = e3 & all_4_3 = e3) | % 12.41/2.52 | | (all_4_0 = e2 & all_4_1 = e2 & all_4_2 = e2 & all_4_3 = e2) % 12.41/2.52 | | % 12.41/2.52 | | BETA: splitting (26) gives: % 12.41/2.52 | | % 12.41/2.52 | | Case 1: % 12.41/2.52 | | | % 12.41/2.52 | | | (27) all_4_0 = e3 & all_4_1 = e3 & all_4_2 = e3 & all_4_3 = e3 % 12.41/2.52 | | | % 12.41/2.52 | | | ALPHA: (27) implies: % 12.41/2.52 | | | (28) all_4_3 = e3 % 12.41/2.52 | | | (29) all_4_2 = e3 % 12.41/2.52 | | | (30) all_4_1 = e3 % 12.41/2.52 | | | (31) all_4_0 = e3 % 12.41/2.52 | | | % 12.41/2.52 | | | COMBINE_EQS: (25), (29) imply: % 12.41/2.52 | | | (32) e3 = e0 % 12.41/2.52 | | | % 12.41/2.52 | | | COMBINE_EQS: (28), (32) imply: % 12.41/2.52 | | | (33) all_4_3 = e0 % 12.41/2.52 | | | % 12.41/2.52 | | | COMBINE_EQS: (30), (32) imply: % 12.41/2.52 | | | (34) all_4_1 = e0 % 12.41/2.52 | | | % 12.41/2.52 | | | COMBINE_EQS: (31), (32) imply: % 12.41/2.52 | | | (35) all_4_0 = e0 % 12.41/2.52 | | | % 12.41/2.52 | | | REF_CLOSE: (9), (25), (33), (34), (35) are inconsistent by sub-proof #1. % 12.41/2.52 | | | % 12.41/2.52 | | Case 2: % 12.41/2.52 | | | % 12.41/2.52 | | | (36) all_4_0 = e2 & all_4_1 = e2 & all_4_2 = e2 & all_4_3 = e2 % 12.41/2.52 | | | % 12.41/2.52 | | | ALPHA: (36) implies: % 12.41/2.52 | | | (37) all_4_3 = e2 % 12.41/2.52 | | | (38) all_4_2 = e2 % 12.41/2.52 | | | (39) all_4_1 = e2 % 12.41/2.52 | | | (40) all_4_0 = e2 % 12.41/2.52 | | | % 12.41/2.52 | | | COMBINE_EQS: (25), (38) imply: % 12.41/2.52 | | | (41) e2 = e0 % 12.41/2.52 | | | % 12.41/2.52 | | | COMBINE_EQS: (37), (41) imply: % 12.41/2.52 | | | (42) all_4_3 = e0 % 12.41/2.52 | | | % 12.41/2.52 | | | COMBINE_EQS: (39), (41) imply: % 12.41/2.53 | | | (43) all_4_1 = e0 % 12.41/2.53 | | | % 12.41/2.53 | | | COMBINE_EQS: (40), (41) imply: % 12.41/2.53 | | | (44) all_4_0 = e0 % 12.41/2.53 | | | % 12.41/2.53 | | | REF_CLOSE: (9), (25), (42), (43), (44) are inconsistent by sub-proof #1. % 12.41/2.53 | | | % 12.41/2.53 | | End of split % 12.41/2.53 | | % 12.41/2.53 | Case 2: % 12.41/2.53 | | % 12.41/2.53 | | (45) (all_4_0 = e1 & all_4_1 = e1 & all_4_2 = e1 & all_4_3 = e1) | % 12.41/2.53 | | (all_4_0 = e0 & all_4_1 = e0 & all_4_2 = e0 & all_4_3 = e0) % 12.41/2.53 | | % 12.41/2.53 | | BETA: splitting (45) gives: % 12.41/2.53 | | % 12.41/2.53 | | Case 1: % 12.41/2.53 | | | % 12.41/2.53 | | | (46) all_4_0 = e1 & all_4_1 = e1 & all_4_2 = e1 & all_4_3 = e1 % 12.41/2.53 | | | % 12.41/2.53 | | | ALPHA: (46) implies: % 12.41/2.53 | | | (47) all_4_3 = e1 % 12.41/2.53 | | | (48) all_4_2 = e1 % 12.41/2.53 | | | (49) all_4_1 = e1 % 12.41/2.53 | | | (50) all_4_0 = e1 % 12.41/2.53 | | | % 12.41/2.53 | | | COMBINE_EQS: (25), (48) imply: % 12.41/2.53 | | | (51) e1 = e0 % 12.41/2.53 | | | % 12.41/2.53 | | | COMBINE_EQS: (47), (51) imply: % 12.41/2.53 | | | (52) all_4_3 = e0 % 12.41/2.53 | | | % 12.41/2.53 | | | COMBINE_EQS: (49), (51) imply: % 12.41/2.53 | | | (53) all_4_1 = e0 % 12.41/2.53 | | | % 12.41/2.53 | | | COMBINE_EQS: (50), (51) imply: % 12.41/2.53 | | | (54) all_4_0 = e0 % 12.41/2.53 | | | % 12.41/2.53 | | | REF_CLOSE: (9), (25), (52), (53), (54) are inconsistent by sub-proof #1. % 12.41/2.53 | | | % 12.41/2.53 | | Case 2: % 12.41/2.53 | | | % 12.41/2.53 | | | (55) all_4_0 = e0 & all_4_1 = e0 & all_4_2 = e0 & all_4_3 = e0 % 12.41/2.53 | | | % 12.41/2.53 | | | ALPHA: (55) implies: % 12.41/2.53 | | | (56) all_4_3 = e0 % 12.41/2.53 | | | (57) all_4_1 = e0 % 12.41/2.53 | | | (58) all_4_0 = e0 % 12.41/2.53 | | | % 12.41/2.53 | | | REF_CLOSE: (9), (25), (56), (57), (58) are inconsistent by sub-proof #1. % 12.41/2.53 | | | % 12.41/2.53 | | End of split % 12.41/2.53 | | % 12.41/2.53 | End of split % 12.41/2.53 | % 12.41/2.53 End of proof % 12.41/2.53 % 12.41/2.53 Sub-proof #1 shows that the following formulas are inconsistent: % 12.41/2.53 ---------------------------------------------------------------- % 12.41/2.53 (1) all_4_3 = e0 % 12.41/2.53 (2) ~ (all_4_0 = e0) | ~ (all_4_1 = e0) | ~ (all_4_2 = e0) | ~ (all_4_3 = % 12.41/2.53 e0) % 12.41/2.53 (3) all_4_1 = e0 % 12.41/2.53 (4) all_4_0 = e0 % 12.41/2.53 (5) all_4_2 = e0 % 12.41/2.53 % 12.41/2.53 Begin of proof % 12.41/2.53 | % 12.41/2.53 | BETA: splitting (2) gives: % 12.41/2.53 | % 12.41/2.53 | Case 1: % 12.41/2.53 | | % 12.41/2.53 | | (6) ~ (all_4_0 = e0) % 12.41/2.53 | | % 12.41/2.53 | | REDUCE: (4), (6) imply: % 12.41/2.53 | | (7) $false % 12.41/2.53 | | % 12.41/2.53 | | CLOSE: (7) is inconsistent. % 12.41/2.53 | | % 12.41/2.53 | Case 2: % 12.41/2.53 | | % 12.41/2.53 | | (8) ~ (all_4_1 = e0) | ~ (all_4_2 = e0) | ~ (all_4_3 = e0) % 12.41/2.53 | | % 12.41/2.53 | | BETA: splitting (8) gives: % 12.41/2.53 | | % 12.41/2.53 | | Case 1: % 12.41/2.53 | | | % 12.41/2.53 | | | (9) ~ (all_4_1 = e0) % 12.41/2.53 | | | % 12.41/2.53 | | | REDUCE: (3), (9) imply: % 12.41/2.53 | | | (10) $false % 12.41/2.53 | | | % 12.41/2.53 | | | CLOSE: (10) is inconsistent. % 12.41/2.53 | | | % 12.41/2.53 | | Case 2: % 12.41/2.53 | | | % 12.41/2.53 | | | (11) ~ (all_4_2 = e0) | ~ (all_4_3 = e0) % 12.41/2.53 | | | % 12.41/2.53 | | | BETA: splitting (11) gives: % 12.41/2.53 | | | % 12.41/2.53 | | | Case 1: % 12.41/2.53 | | | | % 12.41/2.53 | | | | (12) ~ (all_4_2 = e0) % 12.41/2.53 | | | | % 12.41/2.53 | | | | REDUCE: (5), (12) imply: % 12.41/2.53 | | | | (13) $false % 12.41/2.53 | | | | % 12.41/2.53 | | | | CLOSE: (13) is inconsistent. % 12.41/2.53 | | | | % 12.41/2.53 | | | Case 2: % 12.41/2.53 | | | | % 12.41/2.53 | | | | (14) ~ (all_4_3 = e0) % 12.41/2.53 | | | | % 12.41/2.53 | | | | REDUCE: (1), (14) imply: % 12.41/2.53 | | | | (15) $false % 12.41/2.53 | | | | % 12.41/2.53 | | | | CLOSE: (15) is inconsistent. % 12.41/2.53 | | | | % 12.41/2.53 | | | End of split % 12.41/2.53 | | | % 12.41/2.53 | | End of split % 12.41/2.53 | | % 12.41/2.53 | End of split % 12.41/2.53 | % 12.41/2.53 End of proof % 12.41/2.53 % SZS output end Proof for theBenchmark % 12.41/2.53 % 12.41/2.53 1937ms %------------------------------------------------------------------------------